I am trying to find a way to assess the relative influence of a model that is a function of four input parameters with distant interactions. The model calculates the number and location of grid cells that burn in a lattice structure on a monthly basis, and the probably of spread is a function of fuel, fuel moisture, topography, and wind direction associated with each cell (Kennedy et al. 2017). All of these metrics change in time and space based on monthly spatial input processed based ecohydrological model responding to prescribed climate sequence. The fire model converts the value of these variables to relative probabilities of fire spread for each day of simulation using methods described in Kennedy et al. 2017, and they can only take on a value from 0 - 1 (they multiply together and have a range of 0 - 1 as well). The fire model outputs data on a monthly basis, and I have 30 replicate simulations, each with 525 years of data accumulated for the climate scenario I am running. My goal is to assess the relative influence imposed by fuel and fuel moisture (both have no interaction with wind direction or topography, however they do interact, and have ulterior influence from the imposed climate and the vegetation) at driving area burned for each fire event. What is a sound statistical method that I can use to look at the relative influence of these two parameters at the area averaged scale?

I thought of two methods, but I am not sure they are that best way to go about this.

Method 1: Conduct linear regression and a Mann-Kendall test for the relationship between area burned (sum of grid cells burned for each fire event) and the average averaged fuel content (as probably of spread), as well as area burned and the area average fuel moisture content (as probability of spread). Then take the average of all simulation replicates and compare the results to see which relationship is stronger.

Method 2: Conducted a linear regression and a Mann-Kendall test for the relationship between area burned and the residual of area averaged fuel and fuel moisture (fuel - fuel moisture as probabilities of spread). Then take the average of all simulations and see if a correlation and monotonic trend exists. However, with this method if both fuel or fuel moisture is highly variable, its likely no trend will emerge, or in other words, it may be more suited for a climate scenario when one of the two variables are held constant.

Does anyone have a better idea on how to do this? Any insight is appreciated, so thank you in advance!